Related papers: Existence and uniqueness of classical solution to …
Since the pioneering work of James E. Broadwell, discrete velocity models (DVMs) have played a fundamental role in approximating the Boltzmann equation and in the analysis of non-equilibrium gas dynamics. Despite their apparent simplicity,…
The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…
We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We show that for homogeneous Dirichlet boundary values and sufficiently…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish…
In this paper, we study the full regularity and well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin or Dirichlet boundary condition in half space. Under Oleinik's monotonicity assumption, we prove…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
This paper is concerned with the Dirichlet initial-boundary value problem of a 2-D parabolic-elliptic system proposed to model the formation of biological transport networks. Even if global weak solutions for this system are known to exist,…
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear…
In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…
We aim to prove a unique solvability of an initial-boundary value problem (IBVP) for a time-fractional wave equation in a rectangular domain. We exploit the spectral expansion method as the main tool and used the solution to Cauchy problems…
For the string baryon model "triangle" the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string…
A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…
This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schr\"odinger equation on the segment. Considering proper periodic…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…
We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that the fields are bounded. In the case…